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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">tuzsut</journal-id><journal-title-group><journal-title xml:lang="ru">Труды учебных заведений связи</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of Telecommunication Universities</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1813-324X</issn><issn pub-type="epub">2712-8830</issn><publisher><publisher-name>СПбГУТ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.31854/1813-324X-2026-12-1-81-115</article-id><article-id custom-type="edn" pub-id-type="custom">TIWBEI</article-id><article-id custom-type="elpub" pub-id-type="custom">tuzsut-769</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ЭЛЕКТРОНИКА, ФОТОНИКА, ПРИБОРОСТРОЕНИЕ И СВЯЗЬ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>ELECTRONICS, PHOTONICS, INSTRUMENTATION AND COMMUNICATIONS</subject></subj-group></article-categories><title-group><article-title>Совместная максимально-правдоподобная оценка времени прихода сигнала в многолучевом канале при позиционировании устройств в сетях LTE</article-title><trans-title-group xml:lang="en"><trans-title>Joint Maximum Likelihood Time-of-Arrival Estimation in Multipath Channels for Device Positioning in LTE Networks</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0008-0659-8126</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Хыа</surname><given-names>Х. К.</given-names></name><name name-style="western" xml:lang="en"><surname>Hua</surname><given-names>H. C.</given-names></name></name-alternatives><bio xml:lang="ru"><p>аспирант кафедры беспроводных технологий и систем Санкт-Петербургского государственного университета телекоммуникаций им. проф. М.А. Бонч-Бруевича  </p></bio><email xlink:type="simple">khya.khk@sut.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5358-1895</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Фокин</surname><given-names>Г. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Fokin</surname><given-names>G. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>доктор технических наук, доцент, заведующий кафедрой беспроводных технологий и систем Санкт-Петербургского государственного университета телекоммуникаций им. проф. М.А. Бонч-Бруевича</p></bio><email xlink:type="simple">fokin.ga@sut.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Санкт-Петербургский государственный университет телекоммуникаций им. проф. М.А. Бонч-Бруевича</institution><country>Россия</country></aff><aff xml:lang="en"><institution>The Bonch-Bruevich Saint Petersburg State University of Telecommunications</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>07</day><month>03</month><year>2026</year></pub-date><volume>12</volume><issue>1</issue><fpage>81</fpage><lpage>115</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Хыа Х.К., Фокин Г.А., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Хыа Х.К., Фокин Г.А.</copyright-holder><copyright-holder xml:lang="en">Hua H.C., Fokin G.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://tuzs.sut.ru/jour/article/view/769">https://tuzs.sut.ru/jour/article/view/769</self-uri><abstract><sec><title>Актуальность</title><p>Актуальность. Несмотря на развитие технологий 5G, использование 4G остается актуальным. Более того, параметры радиоинтерфейса LTE лежат в основе NR, что делает результаты, полученные для LTE, применимыми и к NR. Позиционирование в сетях LTE основано на измерениях времени прихода сигналов ToA. Условия отсутствия прямой видимости в многолучевом канале вызывают значительные ошибки оценки ToA и требуют разработки методов их компенсации для повышения точности позиционирования. </p><p>Целью работы является повышение точности измерений ToA в условиях отсутствия прямой видимости за счет исследования и разработки методов совместной максимально-правдоподоподобной оценки JML ToA в многолучевом канале. </p></sec><sec><title>Результаты</title><p>Результаты. Показано, что использование метода 2D-JML более эффективно по сравнению с 1D-JML, особенно в сценариях с близкорасположенными многолучевыми компонентами, характерными для сигналов с малой полосой частот. Улучшение достигается при научно обоснованном выборе числа отсчетов сигнала на выходе многолучевого канала. Установлено, что в моделях EPA, EVA и ETU при   после устранения интерференции точность дальномерных измерений методом 2D-JML с гибридной моделью отсчетов составляет от 26 до 60 м для полосы 1,4 МГц и менее 4 м для 20 МГц.</p></sec><sec><title>Новизна</title><p>Новизна. Впервые представлено комплексное научное обоснование ширины полосы и числа отсчетов для метода совместной максимально-правдоподобной оценки ToA в многолучевом канале в типовых сценариях позиционирования устройств LTE для достижения метровой точности дальномерных измерений.</p></sec><sec><title>Теоретическая значимость</title><p>Теоретическая значимость. Уточняются теоретические основы оценки времени прихода сигнала в многолучевых каналах LTE. Предложенный метод JML оценки ToA развивает классический метод максимально правдоподобия, учитывая структуру канала и позволяя приблизиться к НГКР. Результаты могут использоваться при дальнейшем развитии теории позиционирования на основе OFDM-сигналов.</p></sec><sec><title>Практическая значимость</title><p>Практическая значимость. Метод JML может быть реализован в существующих устройствах LTE/LTE-A для повышения точности позиционирования без изменения инфраструктуры сети. Полученные результаты применимы и для разработки алгоритмов позиционирования в перспективных сетях 5G.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Relevance</title><p>Relevance. Despite the development of 5G technologies, the use of 4G remains relevant. Moreover, the LTE radio interface parameters underlie NR, making the results obtained for LTE applicable to NR. Positioning in LTE networks is based on ToA signal arrival time measurements. Non-line-of-sight conditions in a multipath channel cause significant ToA estimation errors, requiring the development of compensation methods to improve positioning accuracy.</p><p>The aim of this work is to improve the accuracy of ToA measurements in non-line-of-sight conditions by researching and developing methods for joint maximum-likelihood (JML) ToA estimation in a multipath channel. </p></sec><sec><title>Results</title><p>Results. The 2D-JML method is shown to be more effective than 1D-JML, especially in scenarios with closely spaced multipath components typical of small-bandwidth signals. This improvement is achieved through a scientifically justified selection of the number of signal samples at the multipath channel output. It was found that in the EPA, EVA, and ETU models at C/N0 = 85 dB∙Hz, after interference elimination, the ranging accuracy of 2D-JML measurements with a hybrid sampling model ranges from 26 to 60 m for a 1.4 MHz bandwidth and less than 4 m for 20 MHz.</p></sec><sec><title>Novelty</title><p>Novelty. For the first time, a comprehensive scientific justification of the bandwidth and number of samples for the joint maximum-likelihood ToA estimation method in a multipath channel is presented in typical LTE device positioning scenarios to achieve meter-level accuracy of ranging measurements.</p><p>The theoretical significance. The theoretical foundations for signal arrival time estimation in multipath LTE channels are refined. The proposed JML ToA estimation method expands on the classical maximum likelihood method by taking into account the channel structure and allowing for closer approximation to the CRLB. The results can be used in the further development of OFDM-based positioning theory.</p><p>The practical significance. The JML method can be implemented in existing LTE/LTE-A devices to improve positioning accuracy without changing the network infrastructure. The results obtained are also applicable to the development of positioning algorithms for future 5G networks.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>позиционирование</kwd><kwd>LTE</kwd><kwd>время прихода сигнала</kwd><kwd>максимально-правдоподобная оценка</kwd><kwd>отсутствие прямой видимости</kwd><kwd>многолучевой канал</kwd><kwd>1D-JML</kwd><kwd>2D-JML</kwd></kwd-group><kwd-group xml:lang="en"><kwd>positioning</kwd><kwd>LTE</kwd><kwd>time of arrival</kwd><kwd>maximum likelihood estimation</kwd><kwd>Non-Line-of-Sight</kwd><kwd>multipath channel</kwd><kwd>1D-JML</kwd><kwd>2D-JML</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено за счет гранта Российского научного фонда № 25-29-01263, https://rscf.ru/project/25-29-01263</funding-statement><funding-statement xml:lang="en">This research was funded by the Russian Science Foundation Grant No. 25-29-01263, https://rscf.ru/project/25-29-01263</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Фокин Г.А., Владыко А.Г. Позиционирование транспортных средств с комплексированием дальномерных, угломерных и инерциальных измерений в расширенном фильтре Калмана // Труды учебных заведений связи. 2021. Т. 7. № 2. С. 51‒67. DOI:10.31854/1813-324X-2021-7-2-51-67. EDN:AIEESO</mixed-citation><mixed-citation xml:lang="en">Fokin G., Vladyko A. Positioning of Vehicles with the Fusion of Time of Arrival, Angle of Arrival and Inertial Measurements in the Extended Kalman Filter. Proceedings of Telecommunication Universities. 2021;7(2):51‒67. (in Russ.) DOI:10.31854/1813-324X-2021-7-2-51-67. EDN:AIEESO</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Лазарев В.О., Фокин Г.А. Оценка точности позиционирования источника радиоизлучения разностно-дальномерным и угломерным методами. Часть 1 // Труды учебных заведений связи. 2019. Т. 5. № 2. С. 88‒100. DOI:10.31854/1813-324X-2019-5-2-88-100. EDN:FFMJWI</mixed-citation><mixed-citation xml:lang="en">Lazarev V., Fokin G. Positioning Accuracy Evaluation of Radio Emission Sources Using Time Difference of Arrival and Angle of Arrival Methods. Part 1. Proceedings of Telecommunication Universities. 2019;5(2):88‒100. (in Russ.) DOI:10.31854/1813-324X-2019-5-2-88-100. EDN:FFMJWI</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Фокин Г.А., Лазарев В.О. Оценка точности позиционирования источника радиоизлучения разностно-дальномерным и угломерным методами. Часть 2. 2D-моделирование // Труды учебных заведений связи. 2019. Т. 5. № 4. С. 65–78. DOI:10.31854/1813-324X-2019-5-4-65-78. EDN:RJHISC</mixed-citation><mixed-citation xml:lang="en">Fokin G., Lazarev V. Positioning Accuracy Evaluation of Radio Emission Sources Using Time Difference of Arrival and Angle of Arrival Methods. Part 2. 2D-Simulation. Proceedings of Telecommunication Universities. 2019;5(4):65‒78. (in Russ.) DOI:10.31854/1813-324X-2019-5-4-65-78. EDN:RJHISC</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Фокин Г.А., Лазарев В.О. Оценка точности позиционирования источника радиоизлучения разностно-дальномерным и угломерным методами. Часть 3. 3D-моделирование // Труды учебных заведений связи. 2020. Т. 6. № 2. С. 87‒102. DOI:10.31854/1813-324X-2020-6-2-87-102. EDN:FKSYIZ</mixed-citation><mixed-citation xml:lang="en">Fokin G., Lazarev V. Positioning Accuracy Evaluation of Radio Emission Sources Using Time Difference of Arrival and Angle of Arrival Methods. Part 3. 3D-Simulation. Proceedings of Telecommunication Universities. 2020;6(2):87‒102. (in Russ.) DOI:10.31854/1813-324X-2020-6-2-87-102. EDN:FKSYIZ</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Wang P., Morton Y.J. Impact Analysis of Intercell Interference in Cellular Networks for Navigation Applications // IEEE Transactions on Aerospace and Electronic Systems. 2023. Vol. 59. Iss. 1. PP. 685‒694. DOI: 10.1109/TAES.2022.3186970. EDN:KIDYAA</mixed-citation><mixed-citation xml:lang="en">Wang P., Morton Y.J. Impact Analysis of Intercell Interference in Cellular Networks for Navigation Applications. IEEE Transactions on Aerospace and Electronic Systems. 2023;59(1):685‒694. DOI:10.1109/TAES.2022.3186970. EDN:KIDYAA</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Wang P. Signal Tracking and Multipath Mitigation for Cellular-Based Positioning // In: Yu K., Lohan E.S., Oppermann I. (eds.) Handbook of Wireless Positioning. Singapore: Springer, 2025. PP. 1‒32. DOI:10.1007/978-981-99-1650-4_62-1</mixed-citation><mixed-citation xml:lang="en">Wang P. Signal Tracking and Multipath Mitigation for Cellular-Based Positioning. In: Yu K., Lohan E.S., Oppermann I. (eds.) Handbook of Wireless Positioning. Singapore: Springer; 2025. p.1‒32. DOI:10.1007/978-981-99-1650-4_62-1</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Wang P., Morton Y.J. Performance comparison of time-of-arrival estimation techniques for LTE signals in realistic multi-path propagation channels // NAVIGATION: Journal of the Institute of Navigation. 2020. Vol. 67. Iss. 4. PP. 691‒712. DOI:10.1002/navi.395. EDN:CVZRIT</mixed-citation><mixed-citation xml:lang="en">Wang P., Morton Y.J. Performance comparison of time-of-arrival estimation techniques for LTE Signals in Realistic Multi-path Propagation Channels. NAVIGATION: Journal of the Institute of Navigation. 2020;67(4):691‒712. DOI:10.1002/navi.395. EDN:CVZRIT</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Фокин Г.А. Процедуры выравнивания лучей устройств 5G NR // Электросвязь. 2022. № 2. С. 26‒31. DOI:10.34832/ELSV.2022.27.2.003. EDN:GWPZQH</mixed-citation><mixed-citation xml:lang="en">Fokin G.A. Beam Alignment Procedures for 5G NR Devices. Elektrosvyaz'. 2022;2:26‒31. (in Russ.) DOI:10.34832/ELSV.2022.27.2.003. EDN:GWPZQH</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Хыа Х.К., Фокин Г.А. Комплексное исследование точности позиционирования устройств в сетях LTE в условиях отсутствия прямой видимости // T-Comm: Телекоммуникации и транспорт. 2025. Т. 19. № 8. С. 13‒28. DOI:10.36724/2072-8735-2025-19-8-13-28. EDN:MJNWRI</mixed-citation><mixed-citation xml:lang="en">Hua H.C., Fokin G.A. Comprehensive study of device positioning accuracy in LTE networks under non-line-of-sight conditions. T-Comm. 2025;19(8):13‒28. (in Russ.) DOI:10.36724/2072-8735-2025-19-8-13-28. EDN:MJNWRI</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Хыа Х.К., Фокин Г.А., Нгуен Х.Н. Позиционирования устройств в сетях LTE. Часть 2. Исследование влияния топологии базовых станций на точность оценок координат // Информационные технологии и телекоммуникации. 2024. Т. 12. № 3. С. 13‒28. DOI:10.31854/2307-1303-2024-12-3-13-28. EDN:KONADC</mixed-citation><mixed-citation xml:lang="en">Hua H.C., Fokin G., Nguyen H.N. Positioning of Devices in LTE Networks. Part 2. Analysis of Base Station Topology Impact on Coordinate Estimation Accuracy. Telecom IT. 2024;12(3):13‒28 (in Russ.) DOI: 10.31854/2307-1303-2024-12-3-13-28. EDN: KONADC</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Хыа Х.К., Фокин Г.А., Рютин К.Е. Позиционирование устройств в сетях LTE. Часть 3. Исследование корреляционных функций опорных сигналов // Информационные технологии и телекоммуникации. 2024. Т. 12. № 4. С. 22‒37. DOI:10.31854/23071303-2024-12-4-22-37. EDN:TFCKCC</mixed-citation><mixed-citation xml:lang="en">Hua H.C., Fokin G., Ryutin K. Positioning of Devices in LTE networks. Part 3. Analysis of Correlation Functions for Reference Signals. Telecom IT. 2024;12(4):22‒37. (in Russ.) DOI:10.31854/2307-1303-2024-12-4-22-37. EDN:TFCKCC</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Shah S.S., Sun C., Yang D., Wisal M., He Y., Lu B., et al. Evaluation of 5G Positioning Based on Uplink SRS and Downlink PRS Under LOS and NLOS Environments // Applied Sciences. 2025. Vol. 15. Iss. 14. P. 7909. DOI:10.3390/app15147909. EDN:MSNWME</mixed-citation><mixed-citation xml:lang="en">Shah S.S., Sun C., Yang D., Wisal M., He Y., Lu B., et al. Evaluation of 5G Positioning Based on Uplink SRS and Downlink PRS Under LOS and NLOS Environments. Applied Sciences. 2025;15(14):7909. DOI:10.3390/app15147909. EDN:MSNWME</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Huang S., Chen H.M., Wang B., Chai J., Wu X., Li F. Positioning Performance Evaluation for 5G Positioning Reference Signal // Proceedings of the 2nd International Conference on Frontiers of Electronics, Information and Computation Technologies (ICFEICT, Wuhan, China, 19‒21 August 2022). IEEE, 2022. PP. 497‒504. DOI:10.1109/ICFEICT57213.2022.00093</mixed-citation><mixed-citation xml:lang="en">Huang S., Chen H.M., Wang B., Chai J., Wu X., Li F. Positioning Performance Evaluation for 5G Positioning Reference Signal. Proceedings of the 2nd International Conference on Frontiers of Electronics, Information and Computation Technologies, ICFEICT, 19‒21 August 2022, Wuhan, China. IEEE; 2022. p.497‒504. DOI:10.1109/ICFEICT57213.2022.00093</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Gireesh N., Seshagiri T., Avula P., Sujatha C.N., Panigrahy A.K., Swaraja K., et al. Reliable TOA and TDOA Location Estimation Under Multipath Fading Channel Conditions in Wideband Wireless Networks for Indoor Factory Applications // Wireless Personal Communications. 2025. Vol. 144. Iss. 1-2. PP. 247–274. DOI:10.1007/s11277-025-11849-6. EDN:CJMWHK</mixed-citation><mixed-citation xml:lang="en">Gireesh N., Seshagiri T., Avula P., Sujatha C.N., Panigrahy A.K., Swaraja K., et al. Reliable TOA and TDOA Location Estimation Under Multipath Fading Channel Conditions in Wideband Wireless Networks for Indoor Factory Applications. Wireless Personal Communications. 2025;144(1-2):247–274. DOI:10.1007/s11277-025-11849-6. EDN:CJMWHK</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Ho K.C., Le T.K. Integrating AOA with TDOA for Joint Source and Sensor Localization // IEEE Transactions on Signal Processing. 2023. Vol. 71. PP. 2087–2102. DOI:10.1109/TSP.2023.3280417. EDN:TAYANG</mixed-citation><mixed-citation xml:lang="en">Ho K.C., Le T.K. Integrating AOA with TDOA for Joint Source and Sensor Localization. IEEE Transactions on Signal Processing. 2023;71:2087–2102. DOI:10.1109/TSP.2023.3280417. EDN:TAYANG</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Al-Odhari A.H.A., Fokin G., Kireev A. Positioning of the Radio Source Based on Time Difference of Arrival Method Using Unmanned Aerial Vehicles // Proceedings of the Conference on Systems of Signals Generating and Processing in the Field of on Board Communications (Moscow, Russia, 14–15 March 2018). IEEE, 2018. DOI:10.1109/SOSG.2018.8350566. EDN:URFGDE</mixed-citation><mixed-citation xml:lang="en">Al-Odhari A.H.A., Fokin G., Kireev A. Positioning of the Radio Source Based on Time Difference of Arrival Method Using Unmanned Aerial Vehicles. Proceedings of the Conference on Systems of Signals Generating and Processing in the Field of on Board Communications, 14–15 March 2018, Moscow, Russia. IEEE; 2018. DOI:10.1109/SOSG.2018.8350566. EDN:URFGDE</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Fokin G., Al-odhari A.H.A. Algorithm for Positioning in Non-Line-of-Sight Conditions Using Unmanned Aerial Vehicles // Proceedings of the 18th International Conference on Next Generation Wired/Wireless Networking (NEW2AN), and 11th Conference on Internet of Things and Smart Spaces (ruSMART), St. Petersburg, Russia, 27–29 August 2018. Lecture Notes in Computer Science. Vol. 11118. Cham: Springer, 2018. PP. 496‒508. DOI:10.1007/978-3-030-01168-0_44. EDN:YAPBHV</mixed-citation><mixed-citation xml:lang="en">Fokin G., Al-odhari A.H.A. Algorithm for Positioning in Non-Line-of-Sight Conditions Using Unmanned Aerial Vehicles. Proceedings of the 18th International Conference on Next Generation Wired/Wireless Networking (NEW2AN), and 11th Conference on Internet of Things and Smart Spaces (ruSMART), 27–29 August 2018, St. Petersburg, Russia. Lecture Notes in Computer Science, vol.11118. Cham: Springer; 2018. p.496‒508. DOI:10.1007/978-3-030-01168-0_44. EDN:YAPBHV</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Peral-Rosado J.A.D., Soualle F., Hofmann A., Heyn T., Querol J., Lapin I. Positioning-Enabled 5G and 6G Satellite Networks: Use Cases and Key Technologies // Proceedings of the 11th Workshop on Satellite Navigation Technology (NAVITEC, Noordwijk, Netherlands, 11‒13 December 2024). IEEE, 2024. DOI:10.1109/NAVITEC63575.2024.10843544</mixed-citation><mixed-citation xml:lang="en">Peral-Rosado J.A.D., Soualle F., Hofmann A., Heyn T., Querol J., Lapin I. Positioning-Enabled 5G and 6G Satellite Networks: Use Cases and Key Technologies. Proceedings of the 11th Workshop on Satellite Navigation Technology, NAVITEC, 11‒13 December 2024, Noordwijk, Netherlands. IEEE; 2024. DOI:10.1109/NAVITEC63575.2024.10843544</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Del Peral-Rosado J.A. Evaluation of the LTE Positioning Capabilities in Realistic Navigation Channels. Ph.D. Dissertation. Bellaterra: Universitat Autònoma de Barcelona, 2014. 164 p.</mixed-citation><mixed-citation xml:lang="en">Del Peral-Rosado J.A. Evaluation of the LTE Positioning Capabilities in Realistic Navigation Channels. Ph.D. Dissertation. Bellaterra: Universitat Autònoma de Barcelona, 2014. 164 p.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Del Peral-Rosado J.A., López-Salcedo J.A., Seco-Granados G., Zanier F., Crisci M. Joint maximum likelihood time-delay estimation for LTE positioning in multipath channels // EURASIP Journal on Advances in Signal Processing. 2014. Vol. 2014. Iss. 1. P. 33. DOI:10.1186/1687-6180-2014-33</mixed-citation><mixed-citation xml:lang="en">Del Peral-Rosado J.A., López-Salcedo J.A., Seco-Granados G., Zanier F., Crisci M. Joint maximum likelihood time-delay estimation for LTE positioning in multipath channels. EURASIP Journal on Advances in Signal Processing. 2014;2014(1):33. DOI:10.1186/1687-6180-2014-33</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Del Peral-Rosado J.A., López-Salcedo J.A., Seco-Granados G., Zanier F., Crisci M. Joint channel and time-delay estimation for LTE positioning reference signals // Proceedings of the 6th ESA Workshop on Satellite Navigation Technologies &amp; European Workshop on GNSS Signals and Signal Processing (NAVITEC, Noordwijk, Netherlands, 5–7 December 2012). IEEE, 2012. DOI:10.1109/NAVITEC.2012.6423094</mixed-citation><mixed-citation xml:lang="en">Del Peral-Rosado J.A., López-Salcedo J. A., Seco-Granados G., Zanier F., Crisci M. Joint channel and time-delay estimation for LTE positioning reference signals. Proceedings of the 6th ESA Workshop on Satellite Navigation Technologies &amp; European Workshop on GNSS Signals and Signal Processing, NAVITEC, 5–7 December 2012, Noordwijk, Netherlands. IEEE; 2012. DOI:10.1109/NAVITEC.2012.6423094</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Del Peral-Rosado J.A., López-Salcedo J.A., Zanier F., Seco-Granados G. Position Accuracy of Joint Time-Delay and Channel Estimators in LTE Networks // IEEE Access. 2018. Vol. 6. PP. 25185‒25199. DOI:10.1109/ACCESS.2018.2827921</mixed-citation><mixed-citation xml:lang="en">Del Peral-Rosado J.A., López-Salcedo J.A., Zanier F., Seco-Granados G. Position Accuracy of Joint Time-Delay and Channel Estimators in LTE Networks. IEEE Access. 2018;6:25185‒25199. DOI:10.1109/ACCESS.2018.2827921</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Wang P., Morton Y.J. Multipath Estimating Delay Lock Loop for LTE Signal TOA Estimation in Indoor and Urban Environments // IEEE Transactions on Wireless Communications. 2020. Vol. 19. Iss. 8. PP. 5518‒5530. DOI:10.1109/TWC.2020.2994037. EDN:TBLAFG</mixed-citation><mixed-citation xml:lang="en">Wang P., Morton Y.J. Multipath Estimating Delay Lock Loop for LTE Signal TOA Estimation in Indoor and Urban Environments. IEEE Transactions on Wireless Communications. 2020;19(8):5518‒5530. DOI:10.1109/TWC.2020.2994037. EDN:TBLAFG</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Dun H., Tiberius C.C.J.M., Janssen G.J.M. Positioning in a Multipath Channel Using OFDM Signals With Carrier Phase Tracking // IEEE Access. 2020. Vol. 8. PP. 13011‒13028. DOI:10.1109/ACCESS.2020.2966070. EDN:FJRCAH</mixed-citation><mixed-citation xml:lang="en">Dun H., Tiberius C.C.J.M., Janssen G.J.M. Positioning in a Multipath Channel Using OFDM Signals With Carrier Phase Tracking. IEEE Access. 2020;8:13011‒13028. DOI:10.1109/ACCESS.2020.2966070. EDN:FJRCAH</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Shamaei K., Khalife J., Kassas Z.M. Exploiting LTE Signals for Navigation: Theory to Implementation // IEEE Transactions on Wireless Communications. 2018. Vol. 17. Iss. 4. PP. 2173‒2189. DOI:10.1109/TWC.2018.2789882</mixed-citation><mixed-citation xml:lang="en">Shamaei K., Khalife J., Kassas Z.M. Exploiting LTE Signals for Navigation: Theory to Implementation. IEEE Transactions on Wireless Communications. 2018;17(4):2173‒2189. DOI:10.1109/TWC.2018.2789882</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Játiva R., Vidal J. Cramer-Rao bounds in the estimation of time of arrival in fading channels // EURASIP Journal on Advances in Signal Processing. 2018. Vol. 2018. P. 19. DOI:10.1186/s13634-018-0540-1</mixed-citation><mixed-citation xml:lang="en">Játiva R., Vidal J. Cramer-Rao bounds in the estimation of time of arrival in fading channels. EURASIP Journal on Advances in Signal Processing. 2018;2018:19. DOI:10.1186/s13634-018-0540-1</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">3GPP TS 36.104. Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS) radio transmission and reception. Release 19. V19.0.9. 2025-03.</mixed-citation><mixed-citation xml:lang="en">3GPP TS 36.104. Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS) radio transmission and reception. Release 19. V19.0.9. 2025-03.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Graff A.M., Humphreys T.E. Ziv-Zakai-Optimal OFDM Resource Allocation for Time-of-Arrival Estimation // IEEE Transactions on Wireless Communications. 2025. Vol. 24. Iss. 8. PP. 6886‒6901. DOI:10.1109/twc.2025.3556788. EDN:WEISRK</mixed-citation><mixed-citation xml:lang="en">Graff A.M., Humphreys T.E. Ziv-Zakai-Optimal OFDM Resource Allocation for Time-of-Arrival Estimation. IEEE Transactions on Wireless Communications. 2025;24(8):6886‒6901. DOI:10.1109/twc.2025.3556788. EDN:WEISRK</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">He J., Ho D.K.C., Xiong W., So H.C., Chun Y.J. Cramér–Rao Lower Bound Analysis for Elliptic Localization With Random Sensor Placements // IEEE Transactions on Aerospace and Electronic Systems. 2024. Vol. 60. Iss. 4. PP. 5587‒5595. DOI:10.1109/TAES.2024.3370890</mixed-citation><mixed-citation xml:lang="en">He J., Ho D.K.C., Xiong W., So H.C., Chun Y.J. Cramér–Rao Lower Bound Analysis for Elliptic Localization With Random Sensor Placements. IEEE Transactions on Aerospace and Electronic Systems. 2024;60(4):5587‒5595. DOI:10.1109/TAES.2024.3370890</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Sun Y., Ho K.C., Xing T., Yang Y., Chen L. Projection-Based Algorithm and Performance Analysis for TDOA Localization in MPR // IEEE Transactions on Signal Processing. 2024. Vol. 72. PP. 896‒911. DOI:10.1109/TSP.2024.3352923. EDN:DFEVWY</mixed-citation><mixed-citation xml:lang="en">Sun Y., Ho K.C., Xing T., Yang Y., Chen L. Projection-Based Algorithm and Performance Analysis for TDOA Localization in MPR. IEEE Transactions on Signal Processing. 2024;72:896‒911. DOI:10.1109/TSP.2024.3352923. EDN:DFEVWY</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Wu W., Wang G., Ho K.C. Multistatic Localization by Differential Time Delays and Time Differences of Arrival in the Absence of Transmitter Position // IEEE Transactions on Aerospace and Electronic Systems. 2023. Vol. 59. Iss. 5. PP. 7020‒7034. DOI:10.1109/TAES.2023.3287814</mixed-citation><mixed-citation xml:lang="en">Wu W., Wang G., Ho K.C. Multistatic Localization by Differential Time Delays and Time Differences of Arrival in the Absence of Transmitter Position. IEEE Transactions on Aerospace and Electronic Systems. 2023;59(5):7020‒7034. DOI:10.1109/TAES.2023.3287814</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">3GPP TR 36.211. Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation. Release 18. V18.0.1. 2024.</mixed-citation><mixed-citation xml:lang="en">3GPP TR 36.211. Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation. Release 18. V18.0.1. 2024.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Yao Y., Zhao K., Jiang Z., Zheng Z., Duan C. High-Precision Time-of-Arrival Estimation Algorithm for 5G-Advanced with Multipath Channel // Circuits, Systems, and Signal Processing. 2024. Vol. 43. PP. 2639–2655. DOI:10.1007/s00034-023-02587-w. EDN:DBUBHI</mixed-citation><mixed-citation xml:lang="en">Yao Y., Zhao K., Jiang Z., Zheng Z., Duan C. High-Precision Time-of-Arrival Estimation Algorithm for 5G-Advanced with Multipath Channel. Circuits, Systems, and Signal Processing. 2024;43:2639–2655. DOI:10.1007/s00034-023-02587-w. EDN:DBUBHI</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Gu H., Zhao K., Yu C., Zheng Z. High resolution time of arrival estimation algorithm for B5G indoor positioning // Physical Communication. 2022. Vol. 50. P. 101494. DOI:10.1016/j.phycom.2021.101494</mixed-citation><mixed-citation xml:lang="en">Gu H., Zhao K., Yu C., Zheng Z. High resolution time of arrival estimation algorithm for B5G indoor positioning. Physical Communication. 2022;50:101494. DOI:10.1016/j.phycom.2021.101494</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Panwar K., Babu P., Stoica P. Maximum Likelihood Algorithm for Time-Delay Based Multistatic Target Localization // IEEE Signal Processing Letters. 2022. Vol. 29. PP. 847‒851. DOI: 10.1109/LSP.2022.3158592. EDN:GSOVJP</mixed-citation><mixed-citation xml:lang="en">Panwar K., Babu P., Stoica P. Maximum Likelihood Algorithm for Time-Delay Based Multistatic Target Localization. IEEE Signal Processing Letters. 2022;29:847‒851. DOI:10.1109/LSP.2022.3158592. EDN:GSOVJP</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Navarro L.A., Tiberius C.C.J.M., Janssen G.J.M. Maximum Likelihood Time-Delay Estimation in Multipath Channels with Two-and Three-Paths Models Using OFDM // Proceedings of the 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS, Salt Lake City, USA, 28 April ‒ 01 May 2025). IEEE, 2025. PP. 968‒979. DOI:10.1109/PLANS61210.2025.11028343</mixed-citation><mixed-citation xml:lang="en">Navarro L.A., Tiberius C.C.J.M., Janssen G.J.M. Maximum Likelihood Time-Delay Estimation in Multipath Channels with Two-and Three-Paths Models Using OFDM. Proceedings of the 2025 IEEE/ION Position, Location and Navigation Symposium, PLANS, 28 April ‒ 01 May 2025, Salt Lake City, USA. IEEE; 2025. p.968‒979. DOI:10.1109/PLANS61210.2025.11028343</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Du J., Cui W., Ba B., Jian C., Zhang L. Joint Estimation for Time Delay and Direction of Arrival in Reconfigurable Intelligent Surface with OFDM // Sensors. 2022. Vol. 22. Iss. 18. P. 7083. DOI:10.3390/s22187083. EDN:MZMJOL</mixed-citation><mixed-citation xml:lang="en">Du J., Cui W., Ba B., Jian C., Zhang L. Joint Estimation for Time Delay and Direction of Arrival in Reconfigurable Intelligent Surface with OFDM. Sensors. 2022;22(18):7083. DOI:10.3390/s22187083. EDN:MZMJOL</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Grover P., Kumar A., Akash, Singh S. K. Channel Estimation for Multi User Massive MIMO Systems Using Federated Learning // Proceedings of the 2nd International Conference on Intelligent Algorithms for Computational Intelligence Systems (IACIS, Hassan, India, 22‒23 August 2025). IEEE, 2025. DOI:10.1109/IACIS65746.2025.11211143</mixed-citation><mixed-citation xml:lang="en">Grover P., Kumar A., Akash, Singh S. K. Channel Estimation for Multi User Massive MIMO Systems Using Federated Learning. Proceedings of the 2nd International Conference on Intelligent Algorithms for Computational Intelligence Systems, IACIS, 22‒23 August 2025, Hassan, India. IEEE; 2025. DOI:10.1109/IACIS65746.2025.11211143</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Kay S.M. Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall PTR, 1993.</mixed-citation><mixed-citation xml:lang="en">Kay S.M. Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall PTR; 1993.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">3GPP TS 36.101. Evolved Universal Terrestrial Radio Access (EUTRA); User Equipment (UE) radio transmission and reception. V19.1.0. 2025-03.</mixed-citation><mixed-citation xml:lang="en">3GPP TS 36.101. Evolved Universal Terrestrial Radio Access (EUTRA); User Equipment (UE) radio transmission and reception. V19.1.0. 2025-03.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Montalbán R., López-Salcedo J.A., Seco-Granados G., Swindlehurst A.L. Power allocation method based on the channel statistics for combined positioning and communications OFDM systems // Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP, Vancouver, Canada, 26–31 May 2013). IEEE, 2013. PP. 4384‒4388. DOI:10.1109/ICASSP.2013.6638488</mixed-citation><mixed-citation xml:lang="en">Montalbán R., López-Salcedo J.A., Seco-Granados G., Swindlehurst A.L. Power allocation method based on the channel sta-tistics for combined positioning and communications OFDM systems. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, 26–31 May 2013, Vancouver, Canada. IEEE; 2013. p.4384‒4388. DOI:10.1109/ICASSP.2013.6638488</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Yang J., Wang X., Park S.I., Kim H.M. Direct path detection using multipath interference cancellation for communication-based positioning system // EURASIP Journal on Advances in Signal Processing. 2012. Vol. 2012. P. 188. DOI:10.1186/1687-6180-2012-188</mixed-citation><mixed-citation xml:lang="en">Yang J., Wang X., Park S.I., Kim H.M. Direct path detection using multipath interference cancellation for communication-based positioning system. EURASIP Journal on Advances in Signal Processing. 2012;2012:188. DOI:10.1186/1687-6180-2012-188</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">3GPP TR 36.942. Evolved Universal Terrestrial Radio Access (E-UTRA); Radio Frequency (RF) system scenarios. Release 19. V19.0.0. 2025-10.</mixed-citation><mixed-citation xml:lang="en">3GPP TR 36.942. Evolved Universal Terrestrial Radio Access (E-UTRA); Radio Frequency (RF) system scenarios. Release 19. V19.0.0. 2025-10.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
